Daniel graduated from the University of Cambridge in 2016 with an MMath degree. He took a range of pure courses in his undergraduate but settled on analysis and probability in his final year. His Part III essay was “Random Walk on Lamplighter Groups”, based on Lyons and Peres’ book “Probability on Trees and Networks”. Daniel enjoys teaching himself foreign languages such as Russian and Japanese, playing the piano, training in the gym, visiting forests and lakes, meeting new friends and learning new sports.

Research project title:
Measure-valued martingales and applications

Supervisor(s):
Alex Cox, Johannes Zimmer

Project description:
Measure-valued martingales are stochastic processes in the space of probability measures which have certain nice martingale properties. They have applications in mathematical finance such as the model-independent pricing and hedging of options. There are natural links to optimal transport and construction of gradient flows for measure-valued processes. They also set up a framework to interpret classical inequalities such as the Log Sobolev Inequality. The aim of Daniel’s PhD project is to establish some basic properties of such processes, and to consider variational methods for their construction.